Two Axes of LLM Abstention: Wrong Answers vs. Unanswerable Questions

A Commonly Confused Distinction

Ask ChatGPT: "Who won the 2024 Nobel Prize in Physics?" It confidently answers: "Einstein." — wrong.

Now ask: "Was Qin Shi Huang the 2024 Nobel Prize in Physics laureate?" It just as confidently answers: "Stephen Hawking." — this time it is not that the answer is wrong; it is that the question should never have been answered in the first place.

Both look like "the model gave a wrong answer," but their nature is entirely different. The first is failing to correctly answer an answerable question — a capability problem. The second is answering a question that shouldn't be answered — a judgment problem.

In July 2026, Benedikt J. Wagner of City St George's, University of London, published a paper on arXiv: Two Axes of LLM Abstention: Answer Correctness and Question Answerability. Through rigorous experiments, it shows that these two failure modes are orthogonal dimensions, and existing abstention mechanisms conflate them.

The Trap of a Single Confidence Score

Mainstream selective answering works like this: the model assigns each response a confidence score and refuses to answer below a threshold. Sounds reasonable — if unsure, say nothing.

But Wagner found this conflates two fundamentally different things:

• Answer correctness: Am I confident in this specific answer?
• Question answerability: Can this question be answered at all?

Using one threshold for both is like using one thermometer to check both "is the food cooked" and "is the room cold" — both are temperature, but the meanings are entirely different.

In a key experiment across five instruction-tuned models (2B to 14B, from three model families), questions were split into three classes:

• C (Correct-answerable): answerable and answered correctly
• W (Wrong-answerable): answerable but answered incorrectly
• U (Unanswerable): cannot be answered (e.g., the Qin Shi Huang Nobel question)

If correctness and answerability were one dimension, C, W, and U should lie along a single line. Instead, they form a crossed geometry: C and W separate along the correctness axis but nearly overlap on the answerability axis; U separates on answerability, while its position on the correctness axis depends on the implementation.

The two axes are independent.

Surface vs. Internal Signals: 0.54 vs. 0.97

The paper's most striking finding concerns where answerability signals live. The author trained two kinds of answerability probes:

1. Output-layer probes: based on output confidence (e.g., softmax of logits) 2. Hidden-layer probes: based on intermediate-layer activations

Results:

• Output-layer probes: AUROC 0.54-0.67 (near chance, with no improvement as models scale)
• Hidden-layer probes: AUROC 0.97-0.99 (near perfect)

This means: the model "knows" whether a question is answerable, but that knowledge is not reflected in its output confidence. Like a person who inwardly recognizes a trap question yet confidently answers anyway — speech and internal judgment are disconnected.

More unsettling: output-layer AUROC shows no significant change from 2B to 14B. Scaling does not make models more honest "on the surface" — it only makes their internal knowledge clearer, without it propagating to output.

CREPE: False Premises in the Wild

The paper also tested the CREPE dataset, built from real Reddit ELI5 questions, some containing false premises — e.g., "Why were there no spectators at the 2020 Tokyo Olympics?" (in fact, there were). These questions look perfectly normal and come from the same distribution as genuine ones.

Results on CREPE:

• Output-layer probes: 0.50-0.54 AUROC (essentially random)
• Elicited self-assessments (P(IK), P(True), direct premise checks): up to 0.67
• Internal linear probes: 0.69-0.77

The gap persists: models can barely detect false premises in their outputs, but hidden layers carry some signal.

From Detection to Repair: 3x Precision Gain

The simplest fix — prompting the model to check premises and refuse when flawed — failed: the model challenged true and false premises at nearly the same rate (57% of false premises challenged, but many true premises wrongly flagged).

Wagner's elegant repair: gate premise checking with the hidden-layer probe:

1. Use the hidden-layer probe to judge answerability 2. Only trigger the premise-check prompt when the probe suspects unanswerability 3. Otherwise, answer directly

Result: challenge precision improved 3x. The model stops challenging legitimate questions and targets suspicious cases precisely — a hybrid approach where the internal probe does coarse filtering and the prompt does fine-grained review.

Dual-Risk Certification: Formalizing Abstention

Wagner reformulates abstention as three-class selective acceptance:

• Accept C (correctly answer answerable questions)
• Reject W (refuse answerable questions you'd get wrong)
• Reject U (refuse unanswerable questions)

with per-class budgets (e.g., α_U = 0.15 misanswered unanswerable, α_W = 0.50 misanswered answerable, δ = 0.10 minimum coverage), certified via exact binomial confidence intervals on a held-out dataset separate from probe training data.

Certification reveals a scale-dependent asymmetry:

• The unanswerable budget certifies on 4 of 5 models
• The answerable budget is bounded by the model's underlying accuracy
• On an 8B model, a factored dual-threshold policy certifies both budgets with 0.75 coverage

A Triage-Desk Analogy

Imagine a hospital triage nurse making two independent judgments: (1) does this patient actually have a condition (answerability), and (2) if so, can we treat it (correctness)? Using a single severity criterion conflates "untreatable serious illness" with "no illness at all." Wagner's scheme mirrors proper triage: the hidden-layer probe screens, the premise check diagnoses.

Limitations

1. Deployment cost of hidden-layer probes: they require internal access, infeasible for closed API models like GPT-4. 2. CREPE performance remains limited: even the best internal probe reaches only 0.77 AUROC. 3. Class boundaries are not sharp: some questions fall between "hard but answerable" and "unanswerable"; hard labels may be overly simplistic. 4. Conservative certification: exact binomial intervals are conservative — a deliberate choice appropriate for safety-critical settings.

The Bigger Picture: Two Dimensions of AI Honesty

The paper points to a deeper question: AI honesty has two layers. Layer one: don't say wrong things (answer correctness). Layer two: know when to stay silent (question answerability). Existing models improve steadily on the first but slowly on the second — and crucially, these layers are independent.

This recalls the Dunning-Kruger effect in humans, but Wagner's finding is subtler: the model knows what it doesn't know — it just doesn't say so. This knowing-but-not-saying gap is a frontier of AI honesty research. The paper's closing line is worth remembering: "Abstention is not one problem." Many seemingly single problems in AI safety turn out to be multidimensional; acknowledging that multidimensionality is the first step toward good safety mechanisms.

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Paper: https://arxiv.org/abs/2607.08456

Author: Benedikt J. Wagner (City St George's, University of London)

Models tested: 5 instruction-tuned models, 2B-14B, from 3 model families

Published: July 9, 2026